This phase I trial studies the side effects and best dose of veliparib when given with or without mitomycin C in treating patients with solid tumors that have spread to other places in the body, cannot be removed by surgery or have come back. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as mitomycin C, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving veliparib together with mitomycin C may kill more tumor cells.